When a motor vehicle tire is to be fit on to or removed from a wheel, such as a disk wheel, which is held in position on a tire-fitting machine, a bead depressor with a plurality of bead depressor elements which are connected together by a cable, that provide for depressing the tire bead into and holding it in the rim well base of the wheel can be used. This fitting tool is of particular advantage more especially when dealing with wide tires having hard side walls. Of the depressor elements which are connected together by the above-mentioned cable, a first depressor element is connected by a holding rod member to a clamping bar, which is fit through a centering bore in the center of the wheel and which is clamped fast to a wheel-mounting assembly of the tire-fitting machine. Therefore, that form of bead depressor can only be used in connection with tire-fitting machines that have a wheel-mounting assembly of a particular configuration, which is suitable for clamping fast the clamping bar.